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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An Hélein’s type convergence theorem for conformal immersions from $\mathbb {S}^{2}$ to manifold
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by Guodong Wei PDF
Proc. Amer. Math. Soc. 147 (2019), 4969-4977 Request permission

Abstract:

In this short paper, we establish an Hélein’s type convergence theorem for conformal immersions from $\mathbb {S}^{2}$ to a general compact Riemannian manifold. As an application, we extend the existence of minimizer of $\int |A|^{2} d\mu$ for immersed 2-spheres in compact 3-manifolds under certain conditions due to E. Kuwert, A. Mondino, and J. Schygulla to higher codimensions.
References
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Additional Information
  • Guodong Wei
  • Affiliation: Key Laboratory of Pure and Applied Mathematics, School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China
  • Email: weiguodong@math.pku.edu.cn
  • Received by editor(s): November 19, 2018
  • Received by editor(s) in revised form: February 24, 2019
  • Published electronically: June 10, 2019
  • Additional Notes: This work was supported by National Natural Science Foundation of China (Grants No. 11671015 and 11731001).
  • Communicated by: Guofang Wei
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4969-4977
  • MSC (2010): Primary 53C42; Secondary 53A30, 53A07
  • DOI: https://doi.org/10.1090/proc/14614
  • MathSciNet review: 4011528